...and whoever is ill or on a journey, the same number [of days which one did not observe Saum (fasts) must be made up] from other days.[Al-Baqarah 2:185]

So, what is incumbent upon this sick person is to fast a number of other days, and if he died before he was able to do that, the obligation is lifted from him, because he did not live until the time which the fast was incumbent upon him. So, he is like one who died in Sha’baan, he is not obliged to fast the approaching month of Ramadan. But if the illness was one from which he was not expected to recover, then the basic principle is that he is obliged to feed a destitute person for each day.